Consider a convergent alternating series with terms satisfying for all and

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider a convergent alternating series with terms

a_n

satisfying

|a_{n+1}|<|a_n|

for all

n

and

\lim_{n\to\infty}a_n=0

. Describe the relationship between the remainder

R_N=S- S_N

and the first omitted term

a_{N+1}